The translation of this treatise is taken from O.Strunk, "Source Readings in Music History" pp.34-46. The date at which Cleonides wrote is unknown; the Oxford Classical Dictionary suggests perhaps the 2nd century A.D. The following paragraph is the translator's introduction.
Of Cleonides we know only that several early manuscripts name him as the author of the little treatise that follows. From his account of the keys, in which there is no mention of Hyperaeolian and Hyperlydian, his French translator Ruelle concludes that he must have lived before the time of Alypius and Aristides Quintilianus (1st century A.D.), the earliest writers to speak of these additions to the Aristoxenian system. Actually, this would seem to suggest just the opposite. As an abbreviator and populariser of Aristoxenus, Cleonides has no reason to mention these additions; the significant thing is that in naming the keys he uses both the Aristoxenian and the later nomenclature. Since the later nomenclature is patently devised for the extended system of fifteen keys, he must have lived after the time when this system was introduced. For the rest, he adheres so closely to Aristoxenus, even in his terminology and wording, that his little abstract is in effect a compensation for the loss of that part of the Aristoxenian writing which has not been preserved. This is in itself enough to dispose of the attribution to Euclid, found in many of the sources, for the teachings of Aristoxenus and of Euclid, in his Division of the Canon, are diametrically opposed. In a Latin translation by Georgius Valla, the 'Eisagōgē' of Cleonides was printed in Venice as early as 1497. It thus became one of the sources from which the musicians of the Renaissance drew their information about the music of Classical Antiquity.
For an explanation of some of the terms used by Cleonides, see the wikipedia articles on the musical system of ancient Greece and pyknon. The Greek text of his treatise, edited by Karl von Jan, is available in archive.org.
[1] Harmonics is the speculative and practical science having to do with the nature of the harmonious. And the harmonious is what is made up of notes and intervals having a certain order. The parts of harmonics are seven: it has to do with notes, intervals, genera, systems (or scales), tones (or keys), modulations, and melodic composition.
[2] The things considered under quality of voice are these. It has two sorts of movements: one is called continuous and belongs to speech, the other is diastematic and belongs to melody. In continuous movement, tensions and relaxations occur imperceptibly and the voice is never at rest until it becomes silent. In diastematic movement, the opposite takes place; the voice dwells on certain points and passes over the distances between them, proceeding first in the one way, then in the other. The points on which it dwells we call pitches, the passages from pitch to pitch we call intervals. The causes of the difference between pitches are tension and relaxation, their effects are height and depth. For the result of tension is to lead toward the high, that of relaxation toward the low. And height is the effect resulting from tension, depth that resulting from relaxation. Pitches are also called notes: one calls them "pitches" (τάσεις) when they are produced by instruments that are struck, because of their being stretched (τετάσθαι); one calls them "notes" (φθόγγοι) when they are produced by the voice. For to be stretched is a property of both. Considered as pitches, the number of notes is infinite; considered as functions, there are in each genus eighteen.
[3] The genera are three: diatonic, chromatic, and enharmonic. The diatonic is sung in descending by tone, tone, and semitone, but in ascending by semitone, tone, and tone. The chromatic is sung in descending by trihemitone, semitone, and semitone, but in ascending by semitone, semitone, and trihemitone. The enharmonic is sung in descending by ditone, diesis, and diesis, but in ascending by diesis, diesis, and ditone.
[4] In the diatonic, chromatic, and enharmonic genera the notes are these:
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Proslambanomenos Hypate hypaton Parhypate hypaton Diatonic lichanos hypaton Hypate meson Parhypate meson Diatonic lichanos meson Mese Trite synemmenon Diatonic paranete synemmenon Nete synemmenon Paramese Trite diezeugmenon Diatonic paranete diezeugmenon Nete diezeugmenon Trite hyperbolaion Diatonic paranete hyperbolaion Nete hyperbolaion |
Proslambanomenos Hypate hypaton Parhypate hypaton Chromatic lichanos hypaton Hypate meson Parhypate meson Chromatic lichanos meson Mese Trite synemmenon Chromatic paranete synemmenon Nete synemmenon Paramese Trite diezeugmenon Chromatic paranete diezeugmenon Nete diezeugmenon Trite hyperbolaion Chromatic paranete hyperbolaion Nete hyperbolaion |
Proslambanomenos Hypate hypaton Parhypate hypaton Enharmonic lichanos hypaton Hypate meson Parhypate meson Enharmonic lichanos meson Mese Trite synemmenon Enharmonic paranete synemmenon Nete synemmenon Paramese Trite diezeugmenon Enharmonic paranete diezeugmenon Nete diezeugmenon Trite hyperbolaion Enharmonic paranete hyperbolaion Nete hyperbolaion |
In the blending of the genera they are these:
Proslambanomenos
Hypate hypaton
Parhypate hypaton
Enharmonic lichanos hypaton
Chromatic lichanos hypaton
Diatonic lichanos hypaton
Hypate meson
Parhypate meson
Enharmonic lichanos meson
Chromatic lichanos meson
Diatonic lichanos meson
Mese
Trite synemmenon
Enharmonic paranete synemmenon
Chromatic paranete synemmenon
Diatonic paranete synemmenon
Nete synemmenon
Paramese
Trite diezeugmenon
Enharmonic paranete diezeugmenon
Chromatic paranete diezeugmenon
Diatonic paranete diezeugmenon
Nete diezeugmenon
Trite hyperbolaion
Enharmonic paranete hyperbolaion
Chromatic paranete hyperbolaion
Diatonic paranete hyperbolaion
Nete hyperbolaion
Of the notes enumerated some are fixed, others movable. The fixed notes are all those that remain unchanged and on the same pitches in the different genera. The movable notes are all those in the opposite case; these do not remain unchanged and on the same pitches in the different genera. The fixed notes are eight, namely the proslambanomenos, hypate hypaton, hypate meson, mese, nete synemmenon, paramese, nete diezeugmenon, and nete hyperbolaion; the movable notes are all those that lie between these.
Of the fixed notes some are barypykna, others lie outside the pykna and bound the perfect systems. Five are barypykna, namely the hypate hypaton, hypate meson, mese, paramese, and nete diezeugmenon. The other three lie outside the pykna and bound the perfect systems, namely the proslambanomenos, nete synemmenon, and nete hyperbolaion.
Of the movable notes some are mesopykna, others are oxypykna, others are diatonic. Five are mesopykna, namely the parhypate hypaton, parhypate meson, trite synemmenon, trite diezeugmenon, and trite hyperbolaion. In each genus five are oxypykna: in the enharmonic genus of enharmonic pykna, in the chromatic genus of chromatic pykna; the diatonic genus does not share in the pyknon. In the enharmonic they are these: the enharmonic lichanos hypaton, enharmonic lichanos meson, enharmonic paranete synemmenon, enharmonic paranete diezeugmenon, and enharmonic paranete hyperbolaion. In the chromatic they are these: the chromatic lichanos hypaton, chromatic lichanos meson, chromatic paranete synemmenon, chromatic paranete diezeugmenon, and chromatic paranete hyperbolaion. In the diatonic they are these: the diatonic lichanos hypaton, diatonic lichanos meson, diatonic paranete synemmenon, diatonic paranete diezeugmenon, and diatonic paranete hyperbolaion.
[5] Of intervals the differences are five, in that they differ from one another in magnitude, and in genus, and as the symphonic from the diaphonic, and as the composite from the incomposite, and as the rational from the irrational. They differ in magnitude in so far as some intervals are larger and others smaller, for example the ditone, tone, semitone, diatessaron, diapente, diapason, and the like. They differ in genus in so far as some intervals are diatonic, others chromatic, and others enharmonic. They differ as the symphonic from the diaphonic in so far as some intervals are symphonic and others diaphonic. The symphonic intervals are the diatessaron, diapente, diapason, and the like. The diaphonic intervals are all those smaller than the diatessaron and all those lying between the symphonic intervals. The intervals smaller than the diatessaron are the diesis, semitone, tone, trihemitone, and ditone; those lying between the symphonic intervals are the tritone, the tetratone, the pentatone, and the like. And symphony is a blending of two notes, a higher and a lower; diaphony, on the contrary, is a refusal of two notes to combine, with the result that they do not blend but grate harshly on the ear. Intervals differ in composition in so far as some are incomposite and others composite. The incomposite intervals are those bounded by consecutive notes, for example the intervals bounded by the hypate and parhypate and by the lichanos and mese; the same applies to the remaining intervals. The composite intervals are those not bounded by consecutive notes, for example the intervals bounded by the mese and parhypate and by the mese and nete and by the paramese and hypate. Thus certain intervals are common to the composite and incomposite, namely those from tlte semitone to the ditone. For the semitone is composite in the enharmonic genus, but incomposite in the chromatic and diatonic; the tone is composite in the chromatic genus, but incomposite in the diatonic; the trihemitone is incomposite in the chromatic genus, but composite in the diatonic; the ditone is incomposite in the enharmonic genus, but composite in the chromatic and diatonic. All intervals smaller than the semitone are incomposite; all intervals larger than the ditone are composite. Intervals differ as the rational from the irrational in so far as some are rational and others irrational. The rational intervals are those whose magnitudes can be defined, such as the tone, semitone, ditone, tritone, and the like. The irrational intervals are those deviating from these magnitudes to a greater or lesser degree by some irrational quantity.
[6] The genera are the three already enumerated. For every melody will be either diatonic or chromatic or enharmonic or common or a mixture of these. The diatonic genus is the one using diatonic division, the chromatic genus the one using chromatic division, the enharmonic genus the one using enharmonic division. The common genus is the one made up of the fixed notes. The mixed genus is the one in which two or three generic characteristics reveal themselves, such as diatonic and chromatic, or diatonic and enharmonic, or chromatic and enharmonic, or diatonic, chromatic, and enharmonic. The differences of the genera arise in connection with the movable notes, for the lichanos is moved within the locus of a tone, the parhypate within that of a diesis. Thus the highest lichanos is that a tone distant from the upper boundary of the tetrachord, the lowest that a ditone distant. In the same way the lowest parhypate is a diesis distant from the lower boundary of the tetrachord, the highest a semitone distant.
[7] Shade is a specific division of a genus. There are six distinct and recognized shades: one enharmonic, three chromatic, and two diatonic.
The shade of the enharmonic uses the division of the genus itself, for it is sung by a diesis equivalent to a quarter-tone, another diesis equal to it, and a ditone.
Of the chromatic divisions, the lowest is the shade of the soft chromatic; it is sung by a diesis equivalent to a third-tone, another diesis equal to it, and the equivalent of a tone plus a half-tone plus a third-tone. The hemiolic chromatic is sung by a hemiolic diesis equivalent to one and one-half times the enharmonic diesis, another diesis equal to it, and an incomposite interval equivalent to seven enharmonic dieses. The tonic chromatic uses the shade of the genus itself, for it is sung by semitone, semitone, and trihemitone. And the chromatic shades just enumerated take their names from their pykna: the tonic chromatic from the tone inherent in its pyknon as a composite interval; the hemiolic chromatic from the hemiolic diesis inherent in its pyknon, one and one-half times the enharmonic diesis; in the same way the soft chromatic is the one having the least pyknon, seeing that its pyknon is relaxed and tuned down.
Of the diatonic divisions one is called soft, the other syntonic. The shade of the soft diatonic is sung by a semitone, an incomposite interval equivalent to three enharmonic dieses, and an interval equivalent to five enharmonic dieses, likewise incomposite. That of the syntonic diatonic shares the division of the genus itself, for it is sung by semitone, tone, and tone.
The shades are also shown by numbers in this manner. The tone is assumed to be divided into twelve least parts, of which each one is called a twelfth-tone. The remaining intervals are also assumed to be divided in the same proportion, the semitone into six twelfths, the diesis equivalent to a quarter-tone into three twelfths, the diesis equivalent to a third-tone into four twelfths, the whole diatessaron into thirty twelfths. In terms of quantity, then, the enharmonic will be sung by 3, 3, and 24 twelfths, the soft chromatic by 4, 4, and 22, the hemiolic chromatic by 4½, 4½ and 21, the tonic chromatic by 6, 6, and 18, the soft diatonic by 6, 9, and 15; the syntonic diatonic by 6, 12, and 12.
[8] Of systems the differences are seven. Four of these were found also in intervals; these are the differences in magnitude, in genus, of the symphonic and diaphonic, and of the rational and irrational. Three differences are peculiar to systems; these are the differences of the progression by step and by leap, of the conjunct and the disjunct, and of the non-modulating and the modulating. In magnitude the larger systems differ from the smaller, as the system of the diapason from that of the tritone or diapente or diatessaron or the like. In genus the diatonic systems differ from the enharmonic or chromatic, or the chromatic or enharmonic from the others. Considered as symphonic or diaphonic, the systems bounded by symphonies will differ from those bounded by diaphonies. Of the systems within the non-modulating system six are symphonic: the smallest is that of the diatessaron, of two tones and a half, for example that from the hypate hypaton to hypate meson; the second, that of the diapente, of three tones and a half, for example that from the proslambanomenos to hypate meson; the third, that of the diapason, of six tones, for example that from the proslambanomenos to mese; the fourth, that of the diapason plus diatessaron, of eight tones and a half, for example that from the proslambanomenos to nete synemmenon or diatonic paranete diezeugmenon; the fifth, that of the diapason plus diapente, of nine tones and a half, for example that from the proslambanomenos to nete diezeugmenon; the sixth, that of the double diapason, of twelve tones, for example that from the proslambanomenos to nete hyperbolaion. The synemmenon system goes only as far as the fourth symphony; in this system the first symphony is that of the diatessaron, the second that of the diapente, the third that of the diapason, the fourth that of the diapason plus diatessaron. But the region of the voice extends to the seventh and eighth symphonies, which are the double diapason plus diatessaron and the double diapason plus diapente. The diaphonic systems are those smaller than that of the diatessaron and all those lying between the symphonic systems.
[9] Figures (or species) of a particular magnitude arise when the order of the simple parts of the given whole undergoes a change with respect to some dissimilar constituent part, the magnitude and number of the parts remaining the same. For when the parts are all equal and similar there is no change in the figures. *2
Of the diatessaron there are three species. The first is that bounded by barypykna, as is that from the hypate hypaton to hypate meson; the second that bounded by mcsopykna, as is that from the parhypate hypaton to parhypate meson; the third that bounded by oxypykna, as is that from the lichanos hypaton to lichanos meson. Thus in the enharmonic and chromatic genera the figures are comprehended in accordance with the nature of the pyknon.
But in the diatonic genus the figures do not occur in connection with a pyknon, for this genus is divided into semitones and tones. The symphony of the diatessaron contains one semitone and two tones; in the same way the diapente contains one semitone and three tones and the diapason two semitones and five tones. In this genus, then, the figures are considered in accordance with the nature of the semitones. Thus in the diatonic genus the first species of the diatessaron is that in which the semitone lies below the tones, the second that in which it lies above the tones, the third that in which it lies between the tones. And these species begin and end with the same notes as in the other genera.
Of the diapente there are four figures. The first, bounded by barypykna, is that in which the tone is at the top; it extends from the hypate meson to paramese. The second, bounded by mesopykna, is that in which the tone is second from the top; it extends from the parhypate meson to trite diezeugmenon. The third, bounded by oxypykna, is that in which the tone is third from the top; it extends from the lichanos meson to paranete diezeugmenon. The fourth, bounded by barypykna, is that in which the tone is at the bottom; it extends from the mese to nete diezeugmenon or from the proslambanomenos to hypate meson.
In the diatonic genus the first figure is that in which the semitone lies at the bottom, the second that in which it lies at the top, the third that in which it is second from the top, the fourth that in which it is third from the top.
Of the diapason there are seven species. The first, bounded by barypykna, is that in which the tone is at the top; it extends from the hypate hypaton to paramese and was called Mixolydian by the ancients.
[10] The second, bounded by mesopykna, is that in which the tone is second from the top; it extends from the parhypate hypaton to trite diezeugmenon and was called Lydian.
The third, bounded by oxypykna, is that in which the tone is third from the top; it extends from the lichanos hypaton to paranete diezeugmenon and was called Phrygian.
The fourth, bounded by barypykna, is that in which the tone is fourth from the top; it extends from the hypate meson to nete diezeugmenon and was called Dorian.
The fifth, bounded by mesopykna, is that in which the tone is fifth from the top; it extends from the parhypate meson to trite hyperbolaion and was called Hypolydian.
The sixth, bounded by oxypykna, is that in which the tone is sixth from the top; it extends from the lichanos meson to paranete hyperbolaion and was called Hypophrygian.
The seventh, bounded by barypykna, is that in which the tone is at the bottom; it extends from the mese to nete hyperbolaion or from the proslambanomenos to mese and was called common or Locrian or Hypodorian.
In the diatonic genus the first species of the diapason is that in which the semitone is first from the bottom but fourth from the top; the second is that in which it is third from the bottom but first from the top; the third is that in which it is second from either end; the fourth is that in which it is first from the bottom but third from the top; the fifth is that in which it is fourth from the bottom but first from the top; the sixth is that in which it is third from the bottom but second from the top; the seventh is that in which it is second from the bottom but third from the top. And these species begin and end with the same notes as in the enharmonic and chromatic genera and were called by the same names.
Considered as rational and irrational, the systems made up of rational intervals will differ from those made up of irrational ones, for those made up of rational intervals are rational, those made up of irrational ones irrational.
Considered as progressing by step and by leap, the systems that are sung by consecutive notes will differ from those that are sung by notes that are not consecutive.
Considered as conjunct and disjunct, the systems put together from conjunct tetrachords will differ from those put together from disjunct. And a conjunction is the note common to two tetrachords of the same species, sung one after another; a disjunction is the tone between two tetrachords of the same species, sung one after another. There are in all three conjunctions: the middle, the highest, and the lowest. The lowest conjunction is that of the tetrachords hypate and meson; the note common to this conjunction is the hypate meson. The middle conjunction is that of the tetrachords meson and neton synemmenon; the note common to this conjunction is the mese. The highest conjunction is that of the tetrachords neton diezeugmenon and hyperbolaion; the note common to this conjunction is the nete diezeugmenon. There is one disjunction, that of the tetrachords meson and neton diezeugmenon; the tone common to this disjunction is that from the mese to paramese.
Of perfect systems there are two, of which one is lesser, the other greater. The Lesser Perfect System is that by conjunction, extending from the proslambanomenos to nete synemmenon. There are in this system three conjunct tetrachords, namely the hypaton, meson, and synemmenon, and there is a tone between the proslambanomenos and hypate hypaton; this system is bounded by the symphony diapason plus diatessaron.
The Greater Perfect System is that by disjunction, extending from the proslambanomenos to nete hyperbolaion. There are in this system four tetrachords, two conjunct pairs mutually disjunct, namely the hypaton and meson and the diezeugmenon and hyperbolaion, and there are two tones, one between the proslambanomenos and hypate hypaton, the other between the mese and paramese; this system is bounded by the symphony double diapason.
Of the five tetrachords in the non-modulating system, which is put together from the two perfect ones, two are common to both the perfect systems: the tetrachords hypaton and meson; peculiar to the conjunct system is the tetrachord neton synemmenon; peculiar to the disjunct system are the tetrachords neton diezeugmenon and hyperbolaion.
[11] Considered as non-modulating and modulating, the systems will differ in so far as the simple systems differ from those that are not simple. The simple systems are those in harmony with one mese, the duple those in harmony with two, the triple those in harmony with three, the multiple those in harmony with many. To be a mese is the function of the note whose property it is, in disjunction, to have above it an incomposite tone (this part of the system remaining unaffected) but below it an incomposite or composite ditone; in conjunction, however, there being three conjunct tetrachords, it is its property to be the highest note of the middle tetrachord or the lowest note of the highest tetrachord. And it is from the mese that the functions of the remaining notes are recognized, for it is clearly in relation to the mese that each of them is thus or thus. *3
[12] The word "tone" is used in four senses: as note, interval, region of the voice, and pitch. It is used in the sense of note in the epithet "seven-toned" as applied to the phorminx, for instance by Terpander and Ion. The former says:
To thee we will play new hymns upon a phorminx of seven tones and will love the four-voiced lay no more; *4
the latter:
Eleven-stringed lyre with thy flight of ten steps into the place where the three concordant roads of Harmonia meet,
Once all the Greeks raised but a meagre music, playing thee seven-toned four by four. *5
And not a few others have used the epithet. We use the word "tone" in the sense of interval whenever we say that it is a tone from the mese to paramese. We use it of the region of the voice whenever we speak of Dorian, or Phrygian, or Lydian, or any of the other tones. According to Aristoxenus there are 13 tones:
Of these the highest is the Hypermixolydian, the lowest the Hypodorian. From the highest to the lowest, the distance between consecutive tones is a semitone, between two parallel tones a trihemitone; with the distance between the remaining tones the case will be similar. The Hypermixolydian is a diapason above the Hypodorian.
We use the word "tone" in the sense of pitch when we speak of using a higher or lower or intermediate tone of voice.
[13] The word "modulation" is used in four senses: with reference to genus, system, tone, and melodic composition. Modulation in genus takes place whenever there is a modulation from the diatonic genus to the chromatic or enharmonic, or from the chromatic or enharmonic to some one of the others. Modulation in system takes place whenever there is a modulation from the conjunct system to the disjunct, or vice versa. Modulation in tone takes place whenever there is a modulation from the Dorian tone to the Phrygian, or from the Phrygian to the Lydian or Hypermixolydian or Hypodorian, or in general whenever there is a modulation from anyone of the thirteen tones to any other. Modulations begin with the semitone and proceed to the diapason, some of them being made by symphonic intervals, others by diaphonic. Those made by symphonic intervals and by that of the tone are melodious. Of the rest, some are more melodious than unmelodious, others less so. For the greater or less the community of elements, the more melodious or unmelodious the modulation, seeing that every modulation requires the presence of some common element, whether a note, an interval, or a system. But this community is determined by the similarity of the notes, for a modulation is melodious or unmelodious in so far as it involves the coincidence of notes that are similar or dissimilar with respect to their participation in a pyknon.
Modulation in melodic composition takes place whenever there is a modulation in ethos from the diastaltic to the systaltic or hesychastic, or from the hesychastic to some one of the others. *6 The diastaltic ethos in melodic composition is that which reveals heroic deeds and the grandeur and loftiness of a manly soul and an affection akin to these. It is most used in tragedy and in all things that border on this character. The systaltic ethos is that by which the soul is brought into dejection and an effeminate condition. Such a state will correspond to erotic affections and to dirges and expressions of pity and things resembling these. The hesychastic ethos is that which accompanies quietude of soul and a liberal and peaceful state. To it will correspond hymns, paeans, eulogies, counsels, and things similar to these.
[14] Melodic composition is the use of the enumerated parts of harmonics, which have the function of subject-matter. Melodic composition is accomplished by means of four figures: succession, plexus or network, repetition or selection, and prolongation. Succession is a progression of the melody by consecutive notes; plexus or network a placing of intervals side by side; repetition or selection a striking of a single tone, repeated several times; prolongation a dwelling for a greater time-interval on a single utterance of the voice.
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